Surface Acoustic Wave (SAW) resonators have been widely applied to the design of surface acoustic wave filters for use in many different communication systems. FIG. 1 depicts a typical SAW resonator, its symbol, and equivalent circuit. The SAW resonator, which generally comprises a transducer embedded between two reflectors, may be fabricated on a single crystal piezoelectric substrate of lithium niobate or lithium tantalate. The transducer is typically a two terminal device with alternating finger electrodes extending from the two opposing bus bars. When an alternating voltage is applied across the bus bars, surface waves are launched generally in a direction normal to the electrodes. The SAW resonator, depending upon the angle cut of the substrate, can either support Raleigh-type surface acoustic waves or leaky shear waves. Using a cut angle of 42° Y-X cut of lithium tantalate, the SAW transducer will predominantly launch leaky shear wave components. It is well known that leaky surface acoustic wave resonators exhibit radiation losses over a range of frequencies. Miyamoto et al. (2002 IEEE Ultrasonics Symposium) has shown a direct observation of the wave radiations extending beyond the normal overlapping area of the transducer aperture into the bus bar regions. When configured as a band pass filter, this radiation of leaky waves into the bus bars is manifested as extra insertion loss at certain frequencies, often causing notches or ripples in the pass band. Depending upon the frequency dependence of the radiation of the leaky waves, the performance degradation may be pronounced near the pass band center or it may occur mostly near one or both pass band edges, thus reducing the usable bandwidth and quality factor, Q, of the filter.
When studying the effects of radiation on single SAW resonators, it is useful to examine the frequency dependent quality factor (Q) of the resonator. Q is defined as the ratio of the stored energy to the dissipated energy in a half cycle. It can be measured in a variety of ways. Q of a resonator can accurately be measured at two specific frequency points as follows:
  Q  =                              1          2                ⁢                  ω          r                ⁢                  ∂                      ∂                                                  ⁢            ω                          ⁢                  (                                    tan                              -                1                                      ⁢                          B              G                                )                    ⁢              ❘                  ω          =                      ω            r                              ⁢                          ⁢      Q        =                            1          2                ⁢                  ω          a                ⁢                  ∂                      ∂                                                  ⁢            ω                          ⁢                  (                                    tan                              -                1                                      ⁢                          B              G                                )                    ⁢              ❘                  ω          =                      ω            a                              where ωr and ωa are the respective resonant and antiresonant frequencies of the resonator, B is the imaginary part of the admittance (denoted susceptance), and G is the real part of the admittance (denoted conductance). FIG. 2 shows a plot of G and B for a typical SAW resonator. The resonant frequency corresponds to the lower of the two frequency points where B crosses zero and undergoes a sign change. From the admittance measurement, Q at exactly two frequency points (ωr and ωa) can be determined. In order to measure the Q at other frequencies, a technique can be employed to arbitrarily shift the resonant or anti-resonant frequency of the filter. The anti-resonant frequency, as shown in FIG. 2, corresponds to the higher zero-crossing frequency of the susceptance, B. By adding or subtracting an arbitrary amount, ΔB, to the susceptance, the anti-resonant frequency can be arbitrarily shifted up or down, as shown in FIG. 3. Qa at each of those frequency points can be measured as described above. For Q measurements below the center of the stop band, a similar technique can be used to shift the resonant frequency. In this case an arbitrary offset is applied to the imaginary part of the impedance (denoted as the reactance, and usually abbreviated X; the real part of the impedance is called the resistance, and is abbreviated R).
By combining the two techniques described above, Q can be measured over a wide frequency range encompassing the entire pass band and beyond. The resonant and anti-resonant Q's in a modeling can be controlled by slightly modifying (“tweaking”) the values of the motional resistance, Rm, and the static conductance, g0. Generally, these “lossy” elements are considered to be constant with frequency. There are certain frequency bands where Q is significantly degraded by some frequency-dependent phenomenon.
While there are several mechanisms at work to degrade the Q (e.g. thin film resistance, elastic and dielectric losses in the substrate, spectral conversion of surface wave energy into bulk modes, etc.), most vary rather slowly with frequency and, therefore, would not be responsible for such volatility in the Q. Instead, the likely culprit is radiation losses. Radiation losses occur at pronounced frequencies where the physical geometry of the resonator permits the resonance of a transversal acoustic mode that radiates energy away from the active area of the resonator. At other nearby frequencies, this same phenomenon can behave in the opposite manner, trapping the energy within the active area, leading to much higher Q's at those frequencies.
FIG. 4 includes a schematic drawing of a typical SAW resonator in which acoustic energy that has leaked out of the active area of the interdigital transducer propagates towards the opposing bus bars. Within the aperture (A) of the transducer, on the other hand, almost no energy leaks out the resonator, because of the reflective gratings of the reflectors at each end. Radiation in leaky surface acoustic wave resonators is difficult to accurately model and is, therefore, quite poorly understood. One method for suppressing the effects of this type of radiation is to increase the aperture of the resonator. As the aperture becomes larger and larger, phenomena taking place at the edges become less and less significant. However, it is not always practical to construct filters using resonators with large apertures. For a constant area providing a fixed capacitance value, an increase in aperture requires a corresponding decrease in length i.e. a reduction in the number of finger pairs of the transducer. This reduction of transducer length results in an increase in spectral losses and resistive losses, both of which adversely affect the Q of the filter.
Shiba et al. (2004 Ultrasonics Symposium) presents yet another method to suppress radiation loss in which the SAW transducer, as depicted in FIG. 5, has a grating of pads connecting to the bus bar. The additional grating bus bar pads effectively reduce the radiation loss. However, it is found, by Shiba et al. that the reduction of radiation is optimized at about one wavelength. Further, an increment in the bus bar grating pad actually has an adverse effect on the loss of the filter.
The effects of radiation can also be compensated in some cases by shifting the transverse resonances to other frequencies where the impact is not as great. Such techniques are largely trial-and-error, and they usually involve much experimentation with various combinations of length, gap and metalization ratio of the active electrodes. Ruile et al. (US 2004/0247153) teaches the technique in which the impact of radiation effect is reduced by varying the gap region and the length of the active electrodes as shown in FIG. 6. However, the varying overlap of the active aperture results in an apodization loss, which would degrade the Q of the resonator.